Based on the parameters of the best-fitting model, a number of substance- and measure-level information graphs were derived. Item response functions (IRFs), indicating the probability of a person with any given trait level endorsing having used a substance, are calculated as pi(θ)=[eai(θ-bi)]/[1+eai(θ-bi)], where θ is a Z-scored trait level, a is the discrimination of the substance (or the slope at the center point where pi(θ)=0.5), and b is the substance location (the horizontal placement of the center point on a z-score scale). Item information functions (IIFs), indicating the information provided by each substance at any trait level, are calculated as Ii(θ)=ai2pi(θ)qi(θ), where qi is 1-pi. Information provided by the entire measure at each trait level is given by the test information function (TIC; T(θ)=ΣIi(θ)). Finally, the standard error of measurement (SEM) at every trait level is SE(θ)=1/T(θ)½ (Embretson & Reise, 2000).
